The term earworm refers the phenomenon of having music stuck in your head. I don't know about you, but often I get a mathworm: an idea or question that simply won't go away. Sometimes a mathworm can take the form of a specific problem that needs solving. Other times it could just be a definition or idea that is particularly attractive. What does this have to do with research?

First, let me ask you a question: what's the best way to find new problems and develop a research plan? I've received lots of advice on this, but there is one strategy that has helped more than any of this advice, and that is: listen to the mathworm!

If there's something in the back of your mind that won't go away, dig it up and satisfy your curiosity about it so you can put it to rest. This strategy has the following two consequences:

Anything that seems to be a continual presence probably means it is the right kind of problem for your brain. This means you'll actually be working on math you like.

A nagging problem or phenomenon in the back of your mind is a distraction from doing other things and so getting rid of it will clear up space for something new. It's sort of like actually listening to what you're hearing in your head makes an earworm go away.